Question

I know the measure of angle m is 100 degrees. I did this multiple times and J and L are not 80 degrees so what are the measures of angles L and J?

Answer 1

Answer:

$m\angle L = 100^{\circ}$.

$m\angle J = 80^{\circ}$.

$m\angle M = 100^{\circ}$.

Step-by-step explanation:

Since segment $JM$ is parallel to segment $KL$, quadrilateral $JKLM$ is a trapezoid.

Segment $JK$ and segment $LM$ (the two legs of this trapezoid) are equal in length. Hence, trapezoid $JKLM$ would be an isoscele trapezoid. By symmetry, $m\angle L = m \angle K = 100^{\circ}$.

Line $JK$ traverses line $JM$ and line $KL$. $\angle J$ and $\angle K$ are a pair of consecutive interior angles as they are both between $JM\!$ and $KL\!$ and are on the same side of the traversal, $JK\!$.

Since line $JM$ is parallel to line $KL$, any pair of consecutive interior angles between these two lines would add up to $180^{\circ}$ (supplementary angles.) Thus, $\angle J$ and $\angle K$ are supplementary angles; $m\angle J + m\angle K = 180^{\circ}$.

Since $m\angle K = 100^{\circ}$, $m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}$.